New Second Order Up-wind Scheme for Oblique Derivative Boundary Value Problem - Medľa, Matej; Mikula, Karol (Proceedings of the Conference Algoritmy, 2016)
This work is devoted to solving the Laplace equation with an oblique derivative prescribed as a boundary condition on a non-uniform logically rectangular grids. Laplace equation is solved using a finite volume method and we use new up-wind type discretization for the oblique derivative. In order to  approximate Laplace equation on non-uniform 3D meshes,the normal derivative is split into the tangential derivative on finite volume faces and derivative in the direction of the vector connecting representative points of finite volumes. New second order up-wind discretization of the oblique derivative, based on linear reconstruction of solution on 3D grid, is presented. A gradient is used for a better approximation of unknown value on the boundary of finite volume. Since both, up-wind and finite volume method, are second order, the whole scheme is second order.